Using an algorithm which is explained in the next sections, we have checked Conjecture REF  for \(p=2\) , \(w\in \lbrace 0,\ldots ,28\rbrace \cup \lbrace 32\rbrace \)  and \(p=3\) , \(w\le 15\) . The case \((p,w)=(2,3)\)  is in fact an exception. Here, the Scopes classes are represented by the cores \(()\) , \((1)\)  and \((2,1)\) . One can show with Magma [1]} that the cores \((1)\)  and \((2,1)\)  correspond to Morita equivalent blocks at least over \(\mathbb {F}_2\) .
